Cyril Catt wrote: [...] Other things being equal, camera lenses of different focal lengths and different effective apertures form an image of the same brightness on the film or sensor if their relative aperture (or f number) is the same. But an f1.4 lens WILL form a brighter image than an f1.8 lens.

That statement is correct. But within the context of this discussion, "other things" are not equal, namely the sensor size and image circle, thus it is wrong to claim LX7's F1.4 is "faster" than RX100's F1.8

The sensor size and the image circle are of no consequence to the amount of brightness with which the lens illuminates a unit area of the sensor.

But we are not comparing a fixed unit area, are we? we are comparing the entire image.

No. we ARE comparing the amount of light falling on a unit area, which results in a specific brightness of illumination, and therefore a specific exposure value. If you spread that light over a greater or lesser area the brightness, and hence the exposure vale, will be different.

As the brightness of the illumination on the sensor depends partly on the distance of the diaphragm from the sensor, it is meaningless to consider only the absolute area of the aperture and to ignore the focal length of the lens. An aperture with an area of 10 square centimetres at a distance of 100 metres from the sensor will provide far less illumination to the sensor than a smaller aperture of one square centimetre at a distance of 10 centimetres from the sensor.

That is correct. because the FOV is vastly different, meaningful comparison can only be done where FOV is the same or at the least similar.

NO. It is related to the inverse square law, which reduces the brightness of illumination in proportion to the inverse of the square of the distance between the diaphragm and the sensor.

As Wikipedia states it: “A lens with a larger maximum aperture (that is, a smaller minimum f-number) is called a "fast lens" because it delivers more light intensity (illuminance) to the focal plane, achieving the same exposure with a faster shutter speed.”

That is only true where FOV and sensor size are the same or similar.

NO AGAIN. The FOV and sensor size are irrelevant. The brightness of illumination of the sensor, and hence the required exposure, is related to the f-number, which is calculated from the focal length of the lens and the effective diameter of the aperture. If the lens is a good quality one it will illuminate the centre and the edge of a large sensor with more or less similar brightness. So if you substitute the sensor with a smaller one, it will also be illuminated with a similar brightness.

May I suggest you look at an exposure meter and take note of the relationships between shutter speed, f-number, ISO, and illumination.

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